Homework Help:
Force on pedals; cyclist up incline

1. The problem statement, all variables and given/known data
A cyclist intends to cycle up a 14-degree inclined hill whose vertical height is 120 m. Assuming the mass of bicycle plus person is 75 kg

a) Calculate how much work is done against gravity

b) A complete revolution of the pedals moves the bike 5.10 m along its path. Calculate the average force that must be exerted on the pedals tangent to their circular path. Neglect work done by friction and other losses. The pedals turn in a circle of diameter 36 cm.

3. The attempt at a solution
The first part wasn't too bad: I got 88200 J.

Second part; I tried using a_tangential = Δv/Δt, but I can't get the time. I'm not sure how to use the radius and the fact that each revolution brings bike 5.10 m forward; I suspect centripetal acceleration formula is somehow involved.

Second part; I tried using a_tangential = Δv/Δt, but I can't get the time. I'm not sure how to use the radius and the fact that each revolution brings bike 5.10 m forward; I suspect centripetal acceleration formula is somehow involved.

You can calculate with average force and constant speed, although the force exerted on the pedals vary during a revolution.
As the bike rolls with constant speed the pedals move with constant angular speed - there is no tangential acceleration.

To get the force applied on the pedals, apply the work-energy theorem again. The bike moves with constant velocity, so the work of gravity + work of the cyclist = 0.
The cyclist exerts force on the pedals along the tangent of the circle of radius 36 cm, and drives the wheel of radius R. The bike rolls. Rolling means that the bike travels a distance equal to the circumference of the circle during one revolution of the wheel. What is the angle between the tangential force and a very small displacement along the arc of a circle? So what is the work of a tangent force when the pedals turn round?